Around 7 percent of registered Democrats voted in the New York City primary runoff last week, in which Councilman John C. Liu of Queens won the party’s nomination for city comptroller and Councilman Bill de Blasio of Brooklyn won the nomination for public advocate.

With such low turnout, the roughly $15 million cost of the runoff meant that the election cost something like $72 per vote cast, according to State Senator Joseph P. Addabbo Jr., a Queens Democrat who announced legislation on Monday to eliminate runoff elections in New York State. Mr. Addabbo’s bill comes after critics have questioned the need for the runoff system, which was created after a New York City mayoral primary 40 years ago.

In both races, the top vote-getter in the primary, held on Sept. 15, won the runoff two weeks later. (In the primary itself, only about 10 percent of registered Democrats cast ballots.)

“I plan to research the process by which run-off elections can be eliminated entirely,” said Mr. Addabbo, who is chairman of the Senate Elections Committee.

“Spending $15 million to hold an election the voters do not wish to participate in is a waste of taxpayer dollars in a time of economic difficulty,” Mr. Addabbo said in a statement. “That money could have instead been spent more wisely, like on our seniors or school children.”
As Sam Roberts reported in The Times recently, runoffs originated in New York City after the 1969 mayoral race, when the Democratic candidate, Mario A. Procaccino, a conservative, was nominated in the primary with only 33 percent of the vote in a five-way race. That November, he was defeated by the incumbent, John V. Lindsay, who was running on the Liberal-Fusion line.

Democratic Party leaders lobbied the Legislature to adopt a runoff for citywide offices beginning in 1973, requiring that a runoff be held if no citywide candidate receives at least 40 percent of the primary vote.

That year, Abraham D. Beame won the mayoral runoff and the general election. Four years later, Edward I. Koch was nominated in a runoff and was elected in November.

Gene Russianoff, a staff lawyer with the New York Public Interest Research Group who has been critical of the runoff system, said the problem did not have an easy solutoin.

“For citywide offices you want someone to have the confidence of the majority of voters,” he said. “But that runs up against the problem and expense of having a runoff with very low turnout, which raises legitimacy questions as well.”

A proposal like Mr. Addabbo’s to simply do away with the runoffs and return to the pre-1969 system runs the risk of a candidate’s winning citywide office with only a tiny plurality of the vote.

A better solution, Mr. Russianoff said, might be an “instant runoff,” in which primary voters cast indicate their top choices by ranking their top choices: No. 1, No. 2, No. 3. If no candidate received at least 40 percent of the No. 1 rankings, an instant runoff would take place between the top two vote-getters by allocating the ballots from the defeated candidates to whichever of the top two candidates was ranked next on that ballot. The candidate with more votes would win.

Such a system is not common in the United States, Mr. Russianoff acknowledged, and “would require a lot of voter education,” but might have the advantage of reducing the administrative expense while addressing the concerns about political legitimacy.

Robert Richie, executive director of FairVote, a nonpartisan organization that researches and promotes electoral reforms, said in a statement that he supported the idea of an instant runoff:

Now that New York is likely to move to new optical scan voting equipment, instant runoff voting is a sensible alternative. It’s been working well in elections in cities with diverse electorates like San Francisco and London and adopted for upcoming elections in Oakland, Minneapolis, Memphis and a growing number of other cities. It’s even going to be used to pick the best picture Oscar this winter. We’ve found that voters like the idea of getting a definitive winner in one round rather than two.

State Senator Liz Krueger, a Manhattan Democrat, has introduced legislation that would allow instant runoff voting in municipal elections in New York State.